The field of invention relates to the measurement of signal waveforms, generally; and, more specifically, to a method and apparatus for accurately determining the crossing point within a logic transition of a differential signal.
FIG. 1a shows an embodiment of a differential signal. A differential signal typically has two signal components. A first signal 102a (usually referred to as the xe2x80x9cpositivexe2x80x9d or xe2x80x9c+xe2x80x9d signal) is indicative of the logical information being transported by the differential signal. A second signal 103a (usually referred to as the xe2x80x9cnegativexe2x80x9d or xe2x80x9cxe2x88x92xe2x80x9d signal) is indicative of the inverse of the logical information being transported by the differential signal.
For example, note that the differential signal observed in FIG. 1a shows a 10101010 data pattern. As such, the + signal 102a is logical xe2x80x9chighxe2x80x9d for each xe2x80x9c1xe2x80x9d in the data pattern and a logical xe2x80x9clowxe2x80x9d for each xe2x80x9c0xe2x80x9d in the data pattern (noting that a logical high voltage is larger than a logical low voltage). Inversely, the xe2x88x92 signal 103a is a logical xe2x80x9clowxe2x80x9d for each xe2x80x9c1xe2x80x9d in the data pattern and a logical xe2x80x9chighxe2x80x9d for each xe2x80x9c0xe2x80x9d in the data pattern.
Note that the 10101010 data pattern of FIG. 1a corresponds to a series of alternating logical values. That is, the logical values of the data pattern repeatedly change from a xe2x80x9c0xe2x80x9d to a xe2x80x9c1xe2x80x9d and from a xe2x80x9c1xe2x80x9d to a xe2x80x9c0xe2x80x9d. Each logical change (which may also be referred to as a logical transition) within FIG. 1a is approximately marked by a vertical line (e.g., noting that a first logical transition is approximately marked by the vertical line positioned at time T1).
FIG. 1b is a depiction of a xe2x80x9czoom inxe2x80x9d of the first logical transition within FIG. 1a (which, as alluded to just above, is approximately positioned at time T1 and corresponds to a transition within the data pattern from a xe2x80x9c1xe2x80x9d to a xe2x80x9c0xe2x80x9d). Note that the logical high voltage is marked as VOH and the logical low voltage is marked as VOL. As such a logical transition from a xe2x80x9c1xe2x80x9d to a xe2x80x9c0xe2x80x9d, as seen in FIG. 1b, typically involves the transitioning of the + signal waveform 102b from VOH to VOL and the xe2x80x94 signal waveform 103b from VOL to VOH (correspondingly, not shown in FIG. 1b, a logical transition from a xe2x80x9c0xe2x80x9d to a xe2x80x9c1xe2x80x9d typically involves the transitioning of the + signal waveform from VOL to VOH and the xe2x88x92 signal waveform from VOH to VOL).
A characteristic of a logical transition within a differential signal is the xe2x80x9ccrossing pointxe2x80x9d of the logical transition. A crossing point 104, as seen in FIG. 1b, corresponds to the voltage where the transitioning + signal waveform 102b and the transitioning xe2x88x92 signal waveform 103b xe2x80x9cmeetxe2x80x9d. That is, if the + signal 102b waveform and the xe2x88x92 signal 103b waveform are overlayed upon another (e.g., with an oscilloscope that samples and displays both waveforms simultaneously) they eventually meet (or cross one another) at the crossing point 104.
FIG. 1b shows an embodiment of an ideally symmetrical logical transition. Indicia of an ideally symmetrical logical transition may include equal rates as between the fall rate of the + signal waveform 102b and the rise rate of the xe2x88x92 signal waveform 103b; and, the + signal waveform 102b begins to fall at the same time the xe2x88x92 signal waveform 103b begins to rise. As a result of these characteristics, the crossing point 104 is positioned approximately midway between VOH and VOL. That is, voltage 105 is the same as voltage 106. Many if not most logical transitions, however, deviate from the ideally symmetrical logical transition observed in FIG. 1b. 
FIG. 2 shows a plurality of crossing points 204a, 204b, 204c that result from the logical transition from a xe2x80x9c1xe2x80x9d to a xe2x80x9c0xe2x80x9d for various pairs of + signal waveforms 202a, 202b, and 202c and xe2x88x92 signal waveforms 203a, 203b, 203c. Specifically: crossing point 204a results from a xe2x80x9c1xe2x80x9d to xe2x80x9c0xe2x80x9d logical transition that comprises + signal waveform 202a and xe2x88x92 signal waveform 203a; crossing point 204b results from a xe2x80x9c1xe2x80x9d to xe2x80x9c0xe2x80x9d logical transition that comprises + signal waveform 202b and xe2x88x92 signal waveform 203b; and crossing point 204c results from a xe2x80x9c1xe2x80x9d to xe2x80x9c0xe2x80x9d logical transition that comprises + signal waveform 202c and xe2x88x92 signal waveform 203c. 
Crossing point 204b and +/xe2x88x92 signal waveform pairs 202b, 203b correspond approximately to the ideally symmetrical logical transition discussed above with respect to FIG. 1b. Crossing points 204a and 204c, however, result from +/xe2x88x92 signal pairs that deviate from an ideally symmetrical relationship. That is, + signal waveform 202a begins to fall significantly after xe2x88x92 signal waveform 203a begins to rise, resulting in a crossing point 204a that is above crossing point 204b. Similarly, + signal waveform 202c begins to fall significantly before xe2x88x92 signal waveform 203c begins to rise, resulting in a crossing point 204c that is below crossing point 204b. 
In light of the fact that many if not most logical transitions deviate from an ideally symmetrical logical transition, it is not uncommon for a differential signal to demonstrate a spread of crossing point positions over time. That is, if a plurality of logical transitions from the same differential signal are overlayed upon one another (as observed in FIG. 2), a plurality of different crossing points 204a, 204b, 204c are likely to be observed.